AI-assisted modeling of capillary-driven droplet dynamics

Abstract In this study, we present and assess data-driven approaches for modeling contact line dynamics, using droplet transport on chemically heterogeneous surfaces as a model system. Ground-truth data for training and validation are generated based on long-wave models that are applicable for slow droplet motion with small contact angles, which are known to accurately reproduce the dynamics with minimal computing resources compared to high-fidelity direct numerical simulations. The data-driven models are based on the Fourier neural operator (FNO) and are developed following two different approaches. The first deploys the data-driven method as an iterative neural network architecture, which predicts the future state of the contact line based on a number of previous states. The second approach corrects the time derivative of the contact line by augmenting its low-order asymptotic approximation with a data-driven counterpart, evolving the resulting system using standard time integration methods. The performance of each approach is evaluated in terms of accuracy and generalizability, concluding that the latter approach, although not originally explored within the original contribution on the FNO, outperforms the former.